
(/VERSIONCHECK 2) 

(DEFPARAMETER |RealRootCharacterizationCategory;CAT| 'NIL) 

(DEFPARAMETER |RealRootCharacterizationCategory;AL| 'NIL) 

(DEFUN |RealRootCharacterizationCategory| (&REST #1=#:G1801)
  (LET (#2=#:G1802)
    (COND
     ((SETQ #2#
              (|assoc| #3=(|devaluateList| #1#)
                       |RealRootCharacterizationCategory;AL|))
      (CDR #2#))
     (T
      (SETQ |RealRootCharacterizationCategory;AL|
              (|cons5|
               (CONS #3#
                     (SETQ #2#
                             (APPLY #'|RealRootCharacterizationCategory;|
                                    #1#)))
               |RealRootCharacterizationCategory;AL|))
      #2#)))) 

(DEFUN |RealRootCharacterizationCategory;| (|t#1| |t#2|)
  (PROG (#1=#:G1800)
    (RETURN
     (PROG1
         (LETT #1#
               (|sublisV|
                (PAIR '(|t#1| |t#2|)
                      (LIST (|devaluate| |t#1|) (|devaluate| |t#2|)))
                (COND (|RealRootCharacterizationCategory;CAT|)
                      ('T
                       (LETT |RealRootCharacterizationCategory;CAT|
                             (|Join| (|SetCategory|)
                                     (|mkCategory|
                                      '(((|sign| ((|Integer|) |t#2| $)) T)
                                        ((|zero?| ((|Boolean|) |t#2| $)) T)
                                        ((|negative?| ((|Boolean|) |t#2| $)) T)
                                        ((|positive?| ((|Boolean|) |t#2| $)) T)
                                        ((|recip|
                                          ((|Union| |t#2| "failed") |t#2| $))
                                         T)
                                        ((|definingPolynomial| (|t#2| $)) T)
                                        ((|allRootsOf| ((|List| $) |t#2|)) T)
                                        ((|rootOf|
                                          ((|Union| $ "failed") |t#2|
                                           (|PositiveInteger|)))
                                         T)
                                        ((|approximate| (|t#1| |t#2| $ |t#1|))
                                         T)
                                        ((|relativeApprox|
                                          (|t#1| |t#2| $ |t#1|))
                                         T))
                                      NIL
                                      '((|PositiveInteger|) (|List| $)
                                        (|Boolean|) (|Integer|))
                                      NIL))
                             . #2=(|RealRootCharacterizationCategory|)))))
               . #2#)
       (SETELT #1# 0
               (LIST '|RealRootCharacterizationCategory| (|devaluate| |t#1|)
                     (|devaluate| |t#2|))))))) 
